Editing Paradox (section)

==Quine's classification<!--"Quine's classification of paradoxes", "Veridical paradox", and "Falsidical paradox" redirect here-->==
{{anchor|Veridical paradox|Falsidical paradox}}

[[W. V. O. Quine]] (1962) distinguished between three classes of paradoxes:<ref>{{cite book | title = The Ways of Paradox, and other essays | last1 = Quine | first1 = W.V. | author-link = W.V. Quine | year = 1966 | publisher = Random House | location = New York | chapter = The ways of paradox | isbn = 9780674948358 |chapter-url=https://books.google.com/books?id=YReOv31gdVIC&q=%22The+ways+of+paradox%22&pg=PA1}}</ref><ref name=Quine>{{Cite book | author=W.V. Quine |title=The Ways of Paradox and Other Essays | location= Cambridge, Massachusetts and London, England | publisher= Harvard University Press | date= 1976 | url=https://math.dartmouth.edu/~matc/Readers/HowManyAngels/WaysofParadox/WaysofParadox.html | edition=REVISED AND ENLARGED}}</ref>

===Veridical paradox===
{{See also|Veridicality}}
A ''veridical paradox'' produces a result that appears counter to [[intuition]], but is demonstrated to be true nonetheless:
* That the Earth is an [[Spherical Earth|approximately spherical object]] that is [[heliocentrism|rotating and in rapid motion around the Sun]], rather than the apparently obvious and common-sensical appearance of the Earth as a stationary [[flat Earth|approximately flat plane]] illuminated by a Sun that [[geocentrism|rises and falls throughout the day]]. 
* [[Condorcet paradox|Condorcet's paradox]] demonstrates the surprising result that [[majority rule]] can be self-contradictory, i.e. it is possible for a majority of voters to support some outcome other than the one chosen (regardless of the outcome itself).
* The [[Monty Hall paradox]] (or equivalently [[three prisoners problem]]) demonstrates that a decision that has an intuitive fifty–fifty chance can instead have a provably different probable outcome. Another veridical paradox with a concise mathematical proof is the [[Birthday problem|birthday paradox]].
* In 20th-century science, [[Hilbert's paradox of the Grand Hotel]] or the [[Ugly duckling theorem]] are famously vivid examples of a theory being taken to a logical but paradoxical end.
* The divergence of the [[harmonic series (mathematics)|harmonic series]]:<math>\sum_{n=1}^\infty\frac{1}{n} = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \cdots.</math>

===Falsidical paradox===

A ''falsidical paradox'' establishes a result that appears false and actually is false, due to a [[fallacy]] in the demonstration. Therefore,  falsidical paradoxes can be classified as [[Fallacy|fallacious arguments]]:
* The various [[invalid proof|invalid mathematical proofs]] are classic examples of this, like the ones that attempt to prove that {{Math|1=1=2}}, which often rely on an inconspicuous [[division by zero]].
* The [[All horses are the same color|horse paradox]], which falsely generalises from true specific statements
* [[Zeno's paradoxes]] are 'falsidical', concluding, for example, that a flying arrow never reaches its target or that a speedy runner cannot catch up to a tortoise with a small head-start.

===Antinomy===

An ''[[antinomy]]'' is a paradox which reaches a self-contradictory result by properly applying accepted ways of reasoning. For example, the [[Grelling–Nelson paradox]] points out genuine problems in our understanding of the ideas of truth and description.

Sometimes described since Quine's work, a ''[[dialetheia]]'' is a paradox that is both true and false at the same time. It may be regarded as a fourth kind, or alternatively as a special case of antinomy. In logic, it is often assumed, following [[Aristotle]], that no ''dialetheia'' exist, but they are allowed in some [[paraconsistent logic]]s.